A member of Miles Davis's legendary second quintet (“arguably Miles's best ever group” according to the Penguin Jazz Guide); a composer of standards (“Watermelon Man”, “Dolphin Dance”, “Maiden Voyage”, “Cantaloupe Island”) and soundtracks (Antonioni's Blow-Up, Bertrand Tavernier's Round Midnight); winner of over 10 Grammy Awards, the first for his 1983 hit single “Rockit”, the most recent for his magnificent 2007 Joni Mitchell tribute album River: The Joni Letters (one of only two jazz recordings to win the coveted Album of the Year award, the other being Getz/Gilberto over 40 years ago). Whichever way you cut it, pianist Herbie Hancock is one of the lodestars of American music, whose influence reaches out far beyond the narrow confines of jazz. A brilliant extended set from this bona fide jazz icon brought a capacity RFH audience to its feet.

There were times during this show when there was so much happening, I didn’t know where to look: at Damon Albarn, driven by musical demons, roaming the stage, singing his heart out, or just grinning, his gold tooth glinting? At the two former members of The Clash who are currently part of the Gorillaz line-up, Mick Jones and Paul Simonon, the latter in particular the absolute epitome of cool in his sailor’s cap and his leather jacket with the collar turned up and his low-slung bass? At the Hypnotic Brass Ensemble, the Chicago band whose swaying horns were such a vital part of the evening? At the silhouetted string section, also in sailors’ caps, lined up across the back of the stage? At Bobby Womack, soul legend and man of infinite dignity, singing “Stylo” (from this year’s Plastic Beach album)?

There were times during this show when there was so much happening, I didn’t know where to look: at Damon Albarn, driven by musical demons, roaming the stage, singing his heart out, or just grinning, his gold tooth glinting? At the two former members of The Clash who are currently part of the Gorillaz line-up, Mick Jones and Paul Simonon, the latter in particular the absolute epitome of cool in his sailor’s cap and his leather jacket with the collar turned up and his low-slung bass? At the Hypnotic Brass Ensemble, the Chicago band whose swaying horns were such a vital part of the evening? At the silhouetted string section, also in sailors’ caps, lined up across the back of the stage? At Bobby Womack, soul legend and man of infinite dignity, singing “Stylo” (from this year’s Plastic Beach album)?

Brad Mehldau is a cool cat. An intellectual one, introverted to the point of semi-autism, precise and clear. A strong mystique based on critic-proof good taste and hardly talking to anyone, least of all many music journalists (I’ve tried). At least that’s what I used to think before last night’s extraordinary show. He still looks a bit of a nerd, hunched over his piano and pale as a baby polar bear locked in the attic for too long, but this was a warm, enveloping trip of a gig. The 21st century is the century the nerds took over - Gates, Zuckerberg, Mehldau. The jocks, the lookers, the sexy ones: your time is up - you really should have been concentrating in algebra, after all.

And we're off. Marking the official start of the London Jazz Festival, “Jazz Voice: Celebrating a Century of Song” provided a superbly paced and brilliantly conceived curtain-raiser. Hosted by Scottish actor Dougray Scott and presenting vocalists from both sides of the Atlantic, this paean to the art of song featured Guy Barker's consummate, high-spec arrangements lovingly performed by his hand-picked orchestra.

There’s a moment during Hjaltalín’s encore when bolero rhythms take over and you wonder if the Reykjavik septet have invented a new musical hybrid: a Ravel-driven makeover of Seventies-slanted soul. As singer Sigrídur Thorlacius lets rip on the thrillingly anthemic “Feels Like Sugar”, it’s clear that Hjaltalín aren’t bothered with current musical templates. They take from the unlikeliest sources, smoosh them together and end up sounding like no one else. After all, this is a band with a stand-up bassoon player.

Bellowhead are 21st-century genre-busters: punk music-hall madness born out of British folk, seasoned with a zeitgeist-friendly dose of multicultural spice. Sounds gimmicky? Well, not at all, as Bellowhead’s greatest quality, apart from being an outstandingly enjoyable live act, comes from the way they ride their eclecticism with brio and intelligence, inventing as they go a new folk music for our times.

So, did they play all the singles? Well no, not all of them, given that they’ve released 26 of the buggers in the past year alone, frisbeeing one out every fortnight in the sort of kamikaze experiment contemplated by only the truly inspired or the slightly desperate. Ash, on the evidence of last night's gig, might just be a bit of both.

I’d not been to the Bloomsbury Ballroom before, but over the past five years or so the likes of Amy Winehouse and Martha Reeves have played this plush Art Deco space. Somewhat disconcertingly, apart from the stage, the rest of the hall was in virtual darkness which suited Dub Colossus perfectly: this intriguing collective of British and Ethiopian musicians are purveyors of intense, atmospheric dance music who actually benefited from this dramatic lack of lighting which made the stage appear to glow like a coal furnace.

Unlikely cool. It’s what unites LCD Soundsystem and Hot Chip. They’re the geeks and outsiders who made it to being hip on the dancefloor. These improbable, subversive electro-pop heroes have united this autumn for what for fans has been a dream double-headline tour. Both bands have had albums out this year and both albums have been well received. But for James Murphy the rumours are that this may be the last tour he does as LCD Soundsystem. And last night he sure was playing as if saying a long goodbye to the ones he’d loved.

Given the somewhat viral nature of Odd Future's rapidly flourishing notoriety, it's both appropriate and a little ironic that their debut UK performance should take place in the basement of a pub in a part of north London where the underground doesn't run. Also known as OFWGKTA (or Odd Future Wolf Gang Kill Them All), this 10-strong self-contained teenage rap conglomerate from Los Angeles has united hip-hop über-nerds, jaded old-schoolers and regular rap fans alike – a remarkable achievement in itself – in praise of unique DIY aesthetic, both musical and visual, inspired by, amongst other things, a love of early Eminem, skateboard culture and the consumption of marijuana.